Assertion- Area of a triangle -ss-as-bs-c where a- b and c are the sides of the triangle and s-a-b-c-2 Reason- Area of a triangle -1-2- base - height Which of the following is correct-

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Byju's Answer

Standard IX

Mathematics

Area of a Triangle - By Heron's Formula

Assertion: Ar...

Question

Assertion: Area of a triangle
$= \sqrt{s (s - a) (s - b) (s - c)}$ where a, b and c are the sides of the triangle and $s = \frac{a + b + c}{2}$

Reason: Area of a triangle $= \frac{1}{2} \times b a s e \times h e i g h t$
Which of the following is correct?

A is true and R is false.

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A is false and R is true.

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Both A and R are true and R is the correct explanation of A.

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Both A and R are true but R is not the correct explanation of A

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Solution

The correct option is D
Both A and R are true but R is not the correct explanation of A

Both Assertion and Reason statements are true but they are two different ways of calculating the area of triangle.

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Similar questions

The area of a triangle, with sides $a, b, c$ and semi-perimeter $s$ , is:

Q. Assertion: The area of an isosceles triangle having base = 24 cm and each of the equal sides equal to 13 cm is 60 cm².
Reason: If 2s = (a + b + c), where a, b, c are the sides of a triangle, then area

= \sqrt{s (s - a) (s - b) (s - c)}

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(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

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Reason: If 2s = (a + b + c), where a, b, c are the sides of a triangle, then area

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Which of the following is correct?

Consider the following two statements

Statements - 1: The area of a right angled triangle
$= \frac{Product of the two sides containing right angle}{2}$

Statement - 2: If the perimeter of a triangle is s and the sides of the triangle are a, b and c respectively then the area of the triangle
$= \sqrt{s (s - a) (s - b) (s - c)}$

Which of the following is true?

Q. Assertion: The sides of a ∆ABC are in the ratio 2 : 3 : 4 and its perimeter is 36 cm. Then,

ar (∆ A B C) = 12 \sqrt{15} {cm}^{2}

.
Reason: If 2s = (a + b + c), where a, b, c are the sides of a triangle, then its area

= \sqrt{(s - a) (s - b) (s - c)}

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Assertion: Area of a triangle =√s(s−a)(s−b)(s−c) where a, b and c are the sides of the triangle and s=a+b+c2 Reason: Area of a triangle =12×base×height Which of the following is correct?

The correct option is D Both A and R are true but R is not the correct explanation of A Both Assertion and Reason statements are true but they are two different ways of calculating the area of triangle.

Assertion: Area of a triangle
$= \sqrt{s (s - a) (s - b) (s - c)}$ where a, b and c are the sides of the triangle and $s = \frac{a + b + c}{2}$

Reason: Area of a triangle $= \frac{1}{2} \times b a s e \times h e i g h t$
Which of the following is correct?

The correct option is D
Both A and R are true but R is not the correct explanation of A

Both Assertion and Reason statements are true but they are two different ways of calculating the area of triangle.